"Despite having one of the all-time great memories I certainly do not remember him," the Republican front-runner declared of New York Times reporter Serge Kovaleski in his statement.

During a Tuesday-night campaign rally, Trump impersonated Kovaleski supposedly retracting a report about the September 11, 2001, attacks. Trump's gestures appeared to many, including The Times and Kovaleski, that he was mocking the reporter's disability, which limits his arm movements.

"We think it's outrageous that he would ridicule the appearance of one of our reporters," a Times spokeswoman told Politico.

According to The Washington Post, the gestures were "all the more personal because Kovaleski covered Trump while reporting for the New York Daily News between 1987 and 1993, a tumultuous period for Trump in which he struggled through several financial setbacks."

But Trump's lengthy statement insisted he had no knowledge of whether Kovaleski was "Muhammad Ali in his prime --- or somebody of less athletic or physical ability."

"His recent statement, to me, seemed like (again without knowing what he looks like) he was groveling and searching for a way out from what he wrote many years ago before," Trump added. "I merely mimicked what I thought would be a flustered reporter trying to get out of a statement he made long ago."

Trump also trashed The Times while demanding an apology:

This is just another example of the dishonest New York Times trying to make a story out of nothing. They should focus on the survival of their newspaper and not on dishonest and very bad reporting about me. The New York Times has become more and more irrelevant and rapidly becoming a total joke — sad!

Several hours after Trump released his statement, The Times published an article in which Kovaleski reiterated that he and Trump knew each other well because he covered Trump for several years as a reporter at the New York Daily News.

"Donald and I were on a first-name basis for years ... I've interviewed him in his office" Kovaleski said. "I've talked to him at press conferences. All in all, I would say around a dozen times, I've interacted with him as a reporter while I was at the Daily News."

Donald trump

(AP Photo/Charlie Neibergall)

The spat started after Trump recently declared that "thousands and thousands" of people were spotted in Jersey City, New Jersey, celebrating the September 11 attacks. Northern New Jersey is home to a large Muslim population.

After a wide range of fact-checkers disputed the claim, Trump pushed back with a September 18, 2001, Washington Post article, written by Kovaleski and another reporter, as evidence.

The two reporters wrote at the time that "authorities detained and questioned a number of people who were allegedly seen celebrating the attacks and holding tailgate-style parties on rooftops while they watched the devastation on the other side of the river."

But they both recently insisted, after Trump made his claim, that their reporting never substantiated the allegations. Trump's Thursday statement said Kovaleski should stand by his years-old report.

"I have tremendous respect for people who are physically challenged and [I] have spent tens of millions of dollars throughout buildings all over the world on making them handicapped accessible," Trump said. "With that being said, Mr. Kovaleski should not have tried to pull back from his statement."

He added:

Over the last number of days, since this issue arose, I have received many phone calls and tweets (@RealDonaldTrump) from people that said I was right about Muslims in New Jersey celebrating the fall of the World Trade Center. Throughout the world it was openly celebrated and so reported.

"Serge Kovaleski must think a lot of himself if he thinks I remember him from decades ago — if I ever met him at all, which I doubt I did," Trump continued in a separate statement. "He should stop using his disability to grandstand and get back to reporting for a paper that is rapidly going down the tubes."

On Wednesday night and Thursday evening, Trump also released a raging tweetstorm against The Times, which had criticized the candidate earlier that day for mocking Kovaleski.

View Trump's full tweetstorm and statement below.

Trump's tweetstorm:

The failing @nytimes should be focused on good reporting and the papers financial survival and not with constant hits on Donald Trump!